Economical Sections. 433 Economical Sections.—It will be seen in Fig. 384 that half the material is incapable of resistance on account of its location near the axis, being only affected by shear, which how- ever, has usually but a small effect. We are therefore driven to the conclusion that ' solid' beams are uneconomical (seen also in the solid circle and triangle in Fig. 385). The hollow circle and hollow rectangle are an improvement, but the best results are obtained by distributing the material near the line of limiting stress, and thus the well-known H section (Fig. 388) is arrived at for wrought'iron, where/c =/t approximately, while the modified T section (Fig. 390) is add^ted for cast iron where fc >/t. Assuming that the vertical web is for the purpose of resisting shear, "we may find the moment of resistance by an Approximate Method.— The direct strength of the flanges forms a couple whose arm may be taken as the depth from centre to centre of the flanges (the vertical web being neglected), Let a = area of total depth of either flange, Moment of resistance of H section =/cach oifta^h whichever is the lowest value. In cast iron j = ^ or J roughly, and the flanges must have /c 4 areas in inverse proportion. Exact graphical solution may also be found, and we will take a few cases.